An official website of the United States government
Flying insects have elastic materials within their exoskeletons that could reduce the energetic cost of flight if their wingbeat frequency is matched to a mechanical resonance frequency. Flapping at resonance may be essential across flying insects because of the power demands of small-scale flapping flight. However, building up large-amplitude resonant wingbeats over many wingstrokes may be detrimental for control if the total mechanical energy in the spring-wing system exceeds the per-cycle work capacity of the flight musculature. While the mechanics of the insect flight apparatus can behave as a resonant system, the question of whether insects flap their wings at their resonant frequency remains unanswered. Using previous measurements of body stiffness in the hawkmoth, Manduca sexta , we develop a mechanical model of spring-wing resonance with aerodynamic damping and characterize the hawkmoth's resonant frequency. We find that the hawkmoth's wingbeat frequency is approximately 80% above resonance and remains so when accounting for uncertainty in model parameters. In this regime, hawkmoths may still benefit from elastic energy exchange while enabling control of aerodynamic forces via frequency modulation. We conclude that, while insects use resonant mechanics, tuning wingbeats to a simple resonance peak is not a necessary feature for all centimetre-scale flapping flyers.
more »
« less
Rapid frequency modulation in a resonant system: aerial perturbation recovery in hawkmoths
Centimetre-scale fliers must contend with the high power requirements of flapping flight. Insects have elastic elements in their thoraxes which may reduce the inertial costs of their flapping wings. Matching wingbeat frequency to a mechanical resonance can be energetically favourable, but also poses control challenges. Many insects use frequency modulation on long timescales, but wingstroke-to-wingstroke modulation of wingbeat frequencies in a resonant spring-wing system is potentially costly because muscles must work against the elastic flight system. Nonetheless, rapid frequency and amplitude modulation may be a useful control modality. The hawkmoth Manduca sexta has an elastic thorax capable of storing and returning significant energy. However, its nervous system also has the potential to modulate the driving frequency of flapping because its flight muscles are synchronous. We tested whether hovering hawkmoths rapidly alter frequency during perturbations with vortex rings. We observed both frequency modulation (32% around mean) and amplitude modulation (37%) occurring over several wingstrokes. Instantaneous phase analysis of wing kinematics revealed that more than 85% of perturbation responses required active changes in neurogenic driving frequency. Unlike their robotic counterparts that abdicate frequency modulation for energy efficiency, synchronous insects use wingstroke-to-wingstroke frequency modulation despite the power demands required for deviating from resonance.
more »
« less
- Award ID(s):
- 1806833
- PAR ID:
- 10282870
- Date Published:
- Journal Name:
- Proceedings of the Royal Society B: Biological Sciences
- Volume:
- 288
- Issue:
- 1951
- ISSN:
- 0962-8452
- Page Range / eLocation ID:
- 20210352
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Flying insects have a robust flight system that allows them to fly even when their forewings are damaged. The insect must adjust wingbeat kinematics to aerodynamically compensate for the loss of wing area. However, the mechanisms that allow insects with asynchronous flight muscle to adapt to wing damage are not well understood. Here, we investigated the phase and amplitude relationships between thorax deformation and flapping angle in tethered flying bumblebees subject to wing clipping and weighting. We used synchronized laser vibrometry and high-speed videography to measure thorax deformation and flapping angle, respectively. We found that changes in wing inertia did not affect thorax deformation amplitude but did influence wingbeat frequency. Increasing wing inertia increased flapping amplitude and caused a phase lag between thorax deformation and flapping angle, whereas decreasing wing inertia did not affect flapping amplitude and caused the flapping angle to lead thorax deformation. Our findings indicate that bumblebees adapt to wing damage by adjusting their wingbeat frequency rather than altering their wing stroke amplitude. Additionally, our results suggest that bumblebees operate near a wing-hinge-dominated resonant frequency, and that moments generated by steering muscles within the wing hinge influence the phase between thorax deformation and wing stroke nontrivially. These insights can inform the design of resilient, insect-inspired flapping-wing micro air vehicles.more » « less
-
Abstract Powering small-scale flapping flight is challenging, yet insects sustain exceptionally fast wingbeats with ease. Since insects act as tiny biomechanical resonators, tuning their wingbeat frequency to the resonant frequency of their springy thorax and wings could make them more efficient fliers. But operating at resonance poses control problems and potentially constrains wingbeat frequencies within and across species. Resonance may be particularly limiting for the many orders of insects that power flight with specialized muscles that activate in response to mechanical stretch. Here, we test whether insects operate at their resonant frequency. First, we extensively characterize bumblebees and find that they surprisingly flap well above their resonant frequency via interactions between stretch-activation and mechanical resonance. Modeling and robophysical experiments then show that resonance is actually a lower bound for rapid wingbeats in most insects because muscles only pull, not push. Supra-resonance emerges as a general principle of high-frequency flight across five orders of insects from moths to flies.more » « less
-
Flying insects are thought to achieve energy-efficient flapping flight by storing and releasing elastic energy in their muscles, tendons, and thorax. However, ‘spring-wing’ flight systems consisting of elastic elements coupled to nonlinear, unsteady aerodynamic forces present possible challenges to generating stable and responsive wing motion. The energetic efficiency from resonance in insect flight is tied to the Weis-Fogh number (N), which is the ratio of peak inertial force to aerodynamic force. In this paper, we present experiments and modeling to study how resonance efficiency (which increases withN) influences the control responsiveness and perturbation resistance of flapping wingbeats. In our first experiments, we provide a step change in the input forcing amplitude to a series-elastic spring-wing system and observe the response time of the wing amplitude increase. In our second experiments we provide an external fluid flow directed at the flapping wing and study the perturbed steady-state wing motion. We evaluate both experiments across Weis-Fogh numbers from 1 < N < 10. The results indicate that spring-wing systems designed for maximum energetic efficiency also experience trade-offs in agility and stability as the Weis-Fogh number increases. Our results demonstrate that energetic efficiency and wing maneuverability are in conflict in resonant spring-wing systems, suggesting that mechanical resonance presents tradeoffs in insect flight control and stability.more » « less
-
In most instances, flapping wing robots have emulated the “synchronous” actuation of insects in which the wingbeat timing is generated from a time-dependent, rhythmic signal. The internal dynamics of asynchronous insect flight muscle enable high-frequency, adaptive wingbeats with minimal direct neural control. In this paper, we investigate how the delayed stretch-activation (dSA) response of asynchronous insect flight muscle can be transformed into a feedback control law for flapping wing robots that results in stable limit cycle wingbeats. We first demonstrate - in theory and simulation - the mechanism by which asynchronous wingbeats self-excite. Then, we implement the feedback law on a dynamically-scaled robophysical model as well as on an insect-scale robotic flapping wing. Experiments on large- and small-scale robots demonstrate good agreement with the theory results and highlight how dSA parameters govern wingbeat amplitude and frequency. Lastly, we demonstrate that asynchronous actuation has several advantages over synchronous actuation schemes, including the ability to rapidly adapt or halt wingbeats in response to external loads or collisions through low-level feedback control.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rspb.2021.0352
